1. Field of the Invention
The present invention relates to color-rendering in a graphical display. In particular, the present invention relates to techniques in rendering highly saturated colors at high luminance in a graphical display (e.g., a light-emitting diode (LED) display) which forms images using three or more basis colors.
2. Discussion of the Related Art
In the electronic displays or signboards used in modern advertising, the images are often provided by light emitting diodes (LEDs). In a typical display, hundreds of thousands to millions of LEDs are used on a typical signboard to produce the multicolored images. The most common basis colors used in such a display are provided by red-, green-, and blue-emitting LEDs. Recently, some graphical displays use more that three basis colors.
In a typical signboard, the LEDs are arranged in small groups, with each group providing a picture element (pixel), which is the basic unit for forming the image that is shown on a graphical display. Each pixel, formed by LEDs of the basis colors is capable of displaying a wide range of colors. The collection of all colors capable of being displayed by a pixel is called a “gamut.” To display any color of the gamut, the LED or LEDs of each basis color are appropriately driven to controlled intensities. The intensity of light emitted from an LED is achieve by controlling the current in the LED. As the human psychovisual system has a frequency response for temporal variations in light intensity that is essentially zero for frequencies greater than about 100 Hz1, the typical LED driver can be modeled as a current source that is pulse modulated to produce two binary states—either zero current or a current of a reference value. In a typical display, such a driver drives either a single LED or a string of serially connected LEDs. The modulation rate is typically chosen so that the waveform has essentially no energy below 100 Hz. In addition, the duty cycle of the waveform is selected so that the average current in the LED or LEDs provide the required light intensity. 1 Light intensity variations at below 100 Hz may result in a “flicker” sensation
At present, most signboards using LEDs control the overall brightness by simply applying a common scaling factor (CSF) to all drivers in the signboard. Furthermore, the maximum luminous intensity usually occurs for a color near a daylight color. These factors together limit the signboard's ability to produce highly saturated colors at night, when the overall brightness is much less than the brightness used during the daytime.
At least three basis colors are required to form a gamut. Using more than three basis colors expands the gamut and introduces additional degrees of freedom that can be exploited for performance improvement. For example, the additional basis colors allow rendering colors located near the boundary of the expanded gamut, which are not available in a three-basis color gamut. An LED signboard which uses more than three basis colors is disclosed, for example, in U.S. Pat. RE 40953 to Paul O. Scheibe, reissued on Nov. 10, 2009, entitled “Light-emitting Diode Display,” which is a reissue of U.S. Pat. No. 6,639,574, issued on Oct. 28, 2003.
FIG. 1 illustrates an example of a color gamut defined by five basis colors. The color gamut is the set of points bounded by the convex hull of points in the plane consisting of the (x, y) CIE chromatic coordinates. As shown in FIG. 1, color gamut 100 is a pentagon with its vertices defined by five basis colors. FIG. 1 uses a representation of colors using the CIE colorimetric system known to those skilled in the art. A detailed description of the CIE colorimetric system may be found, for example, in Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd Edition, by Gunter Wyszecki and W. S. Stiles, John Wiley & Sons, Inc., New York (1982). For a discussion of the CIE colorimetric system, see, especially, pages 130-248 and 137-142.
In the detailed description below, the CIE XYZ (tristimuli) colorimetric system and the CIE chromaticity coordinate system are used. Under the CIE XYZ (tristimulus) colorimetric system, the color of a given pixel is described by CIE XYZ coordinates (X, Y, Z). The basic colorimetric equations for the additive color mixture in an LED type color display are:
                                          ∑                          p              =              1                        P                    ⁢                                    b              p                        ⁢                          X              p                                      =        X                                      1          ⁢          a                )                                                      ∑                          p              =              1                        P                    ⁢                                    b              p                        ⁢                          Y              p                                      =        Y                                      1          ⁢          b                )                                                      ∑                          p              =              1                        P                    ⁢                                    b              p                        ⁢                          Z              p                                      =        Z                                      1          ⁢          c                )            where the color display is formed by pixels each containing P basis color LEDs or strings of LEDs, with the p-th basis color having CIE XYZ coordinates (Xp, Yp, Zp) at maximum luminous intensity, and where the LED drive coefficient 0≦bp≦1 providing linear luminous intensity control for basis colors p=1, . . . , P. Using vector-matrix notation, equations (1)-(3) may be compactly rewritten as (a bold lower-case letter denotes a vector):Ab=v  2a)Where
                    A        =                  [                                                                      X                  1                                                            …                                                              X                  p                                                            …                                                              X                  P                                                                                                      Y                  1                                                            …                                                              Y                  p                                                            …                                                              Y                  P                                                                                                      Z                  1                                                            …                                                              Z                  p                                                            …                                                              Z                  P                                                              ]                                              2          ⁢          b                )            and
                    b        =                                            [                                                                                          b                      1                                                                                                            …                                                                                                              b                      2                                                                                                            …                                                                                                              b                      3                                                                                  ]                        ⁢                                                  ⁢            and            ⁢                                                  ⁢            v                    =                      [                                                            X                                                                              Y                                                                              Z                                                      ]                                                        2          ⁢          c                )            Addition notational and background information may be found, for example, at (a) R. Bellman, Introduction to Matrix Analysis, Second Edition, McGraw-Hill Book Company, New York (1970); (b) Roger A. Horn and Charles R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge (1988) and (c) Jan R. Magnus and Heinz Neudecker, Matrix Differential Calculus, John Wiley & Sons, Inc., New York (1988).
Alternatively, the CIE chromaticity coordinates (x, y, z) may be used. The chromaticity coordinates (x, y, z) satisfy
                    x        =                  X                      X            +            Y            +            Z                                                        3          ⁢          a                )                                y        =                  Y                      X            +            Y            +            Z                                                        3          ⁢          b                )                                z        =                  Z                      X            +            Y            +            Z                                                        3          ⁢          c                )            (See, for example, Gunter Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd Edition, John Wiley & Sons, Inc., New York (1982), page 139.) Since x+y+z=1, the pair (x, y) is also sometimes used under the CIE chromaticity coordinates system to designate the color. The value of the third coordinate (z=1−x−y) is implicitly provided. Color (x, y) and luminous intensity Y may also be represented by the triple (x, y, Y). The chromaticity coordinates are related to the CIE XYZ coordinates by:
                    X        =                              x            y                    ⁢          Y                                              4          ⁢          a                )                                Y        =                              y            y                    ⁢          Y                                              4          ⁢          b                )                                Z        =                              z            y                    ⁢          Y                                              4          ⁢          c                )            
Given the matrix A of basis color specifications, as defined in Equation 2b), the maximum luminous intensity Ŷ and associated control vector {circumflex over (b)} may be calculated given the chromaticity coordinates (x, y) and the constraints. The resulting drive vector {circumflex over (b)} can be scaled to correspond to any other choice of luminous intensity. (The chromaticity coordinates are invariant to the scaling, as can be seen from equations 3a)-3c)). If the chromaticity coordinates (x, y) of the desired color v are within the color gamut provided by the LED strings, then Eq. 2a) has solution such that all elements of b are non-negative; otherwise, the desired pixel color or luminous intensity cannot be achieved, and some approximation to the color is necessary.
Returning to FIG. 1, the chromaticity coordinates (x, y, Y) of the five vertices of color gamut 100 are blue at (0.13, 0.07, 1.56), cyan at (0.085, 0.490, 2.2), green at (0.16, 0.71, 2.92), green-yellow at (0.25, 0.70, 2.56) and red at (0.70, 0.30, 2.56). Each additional basis color increases the size of the color gamut. In this example, color gamut 100 includes three triangles 101, 102 and 103. In one implementation, color gamut 100 defines 40200 colors, with about 3700 colors in triangle 101, 4000 colors in triangle 102 and 32500 colors in triangle 103, at ΔEab=1 level (i.e., the resolution at which a trained human observer can detect a subtle difference in shade) with constant luminance at Y=60. With three basis colors, a unique combination of LED drive currents produces a given color and a given luminous intensity. However, with more than three basis colors, the specified color and luminous intensity can usually be achieved by more than one combination of drive currents in the basis LEDs. Further conditions or constraints may be advantageously imposed on these drive current combinations.